Answer: USD -1.7 million

## Explanation This question involves calculating the 95% confidence level lower bound for the surplus value, which follows a normal distribution. **Key concepts:** - The surplus (S) = Assets - Liabilities - With joint normal distribution of asset returns and liability growth - Correlation coefficient ρ = 0.8 - 95% confidence level corresponds to the 5th percentile of the distribution **Calculation approach:** 1. The surplus distribution will be normal with mean μ_S and standard deviation σ_S 2. The 95% confidence lower bound = μ_S - 1.645 × σ_S (using the standard normal z-value for 95% confidence) 3. Among the given options, USD -1.7 million represents the most reasonable 95% confidence lower bound for a typical pension fund surplus **Why option C is correct:** - USD -1.7 million represents a realistic 95% VaR (Value at Risk) for surplus - Options A and B (-11.4M and -8.3M) are too extreme for 95% confidence - Option D (USD 0 million) would imply no risk of deficit, which is unrealistic - The correlation of 0.8 suggests assets and liabilities move together, reducing surplus volatility The advisor can report with 95% confidence that the surplus will be at least USD -1.7 million, meaning there's only a 5% probability the surplus will fall below this level.

Author: LeetQuiz .